Klinsmann's men took the lead at Craven Cottage in London, where Sunderland's Altidore converted a 10th-minute penalty.
But the South Americans prevailed after second-half goals to Carlos Bacca and Teofilo Gutierrez.
Altidore, who is yet to start in the Premier League this season, scored his 25th goal for the USA, and Klinsmann said he was hoping Sunderland boss Gus Poyet would look positively on his striker's performance.
"All we can do is to keep our fingers crossed, that he can convince the coach. But it's not on us," Klinsmann said of Altidore, who has played just 81 league minutes in six substitute appearances.
"We know when he comes to us [the national team], he's full of energy, he loves the spirit here, he's one of our most experienced players.
"And tonight, when he had more and more one-on-one situations, he proved that he can be a real handful.
"And hopefully this helps him too, it gives him a little more confidence. This is the Jozy Altidore that we know."
Altidore refused to hit out at Poyet despite his uplifting performance, claiming he is happy at the Wearside club.
"It is what it is," the former AZ man said of his lack of club game time.
"I always feel honoured to have the opportunity to play for the national team.
"I have nothing bad to say about my club, I have a good manager."
On debutant and strike partner Rubio Rubin, Altidore said the experience of playing against a world football powerhouse would only serve him well.
Rubin was substituted in the 67th minute, after helping earn the penalty for the US - he pressured Pablo Armero under the ball, and the defender threw his left arm out and was penalised accordingly.
"I thought it was great for him, for an 18-year-old to make his first start against the number three side in the world," Altidore said.
"I thought he did more than OK. It's a great step for him, now he knows what's expected of him at this level, what it takes."
Altidore added: "I'm always talking to Rubio, when I'm in England I send him messages, because he has a talent, you can see that. I'm happy for him.
"He works really hard and he has that knack of being in the right place in the right time. And that helps me."
